Data Sufficiency

If x and y are non-zero integers and |x| + |y| = 32, what is xy?
(1) -4x - 12y = 0
(2) |x| - |y| = 16

..The Answer is A. However, I am confused by the explanation below:


(1) SUFFICIENT: Statement (1) can be rephrased as follows:

-4x - 12y = 0
-4x = 12y
x = -3y

If x and y are non-zero integers, we can deduce that they must have opposite signs: one positive, and the other negative. Therefore, this last equation could be rephrased as

|x| = 3|y| {WHY DO THIS STEP? WHY DOES THIS MAKE SENSE?}

We don't know whether x or y is negative, but we do know that they have the opposite signs. Converting both variables to absolute value cancels the negative sign in the expression x = -3y.

We are left with two equations and two unknowns, where the unknowns are |x| and |y|:

|x| + |y| = 32
|x| - 3|y| = 0

Subtracting the second equation from the first yields

4|y| = 32
|y| = 8

Substituting 8 for |y| in the original equation, we can easily determine that |x| = 24. Because we know that one of either x or y is negative and the other positive, xy must be the negative product of |x| and |y|, or -8(24) = -192.

This is how I figured it out....

If -4x * 12y = 0,

then either x or y MUST equal 0.

Hence xy ALWAYS equal to 0.

Oops misread question.

What the explanation is saying is that it does not matter which variable is negative. We are trying to find xy. Since we know that one and only one of them is negative, it does not matter which one. Hence, all that matters is knowing the relationship between the absolute value of the variables.